home workout routine?

Hello,

Before i get into my routine/questions, let me just quickly describe myself. 19 years old, never really worked out before and at the moment am really quite busy with school. I don't think i can really make the time/commitment to going to a gym somewhere- i think i'd prefer working out at home anyways(i've never been inside a gym in my life) 6ft 3 and 160lbs. I desperately want to get bigger(mainly chest and arms but i dont want to look disproportionate either), and i think i have the motivation and focus required to do so. I'm thinking my goal would be 180-190lbs.

So i'd like to do this at home. That being said, i know i don't have the required equipment. All i have is 3 sets of dumbbells:10lbs, 20 and 25lbs. I'm not looking to spend a fortune here, hopefully you guys have some good ideas for a routine that can help me towards my goal, requiring as little new equipment purchases as possible..

I'm a total newbie when it comes to working out, and while i have been reading quite a bit of articles, i know your advice would be helpful.
Nutrition/diet i think i have some really good ideas, there are tons of articles out there to help with that. I'd like your personal advice on my routine below that i've been trying out for the past few weeks:

I do this every two days. It takes me about an hour and a half, sometimes less. I hope i have the terminology right for some of these exercises, but you get the idea:

3 sets of 20-25 pushups
3 sets of 10-15 25lb bicep curls
3 sets of 10-12 20lb tricep curls
3 sets of 20-25 25lb wrist curls
3 sets of 15-20 20lb dumbbell fly
3 sets of 15-20 25lb dumbbell press(? i lie on my back and with a dumbbell in each arm push straight up and straight down)
3 sets of 10-15 25lb shrugs(Dumbbell Shrug)
3 sets of 10-15 25lb dumbbell bent over rows(Dumbbell Bent-over Row)

and that's about it. Generally i like to repeat a few of these exercises after i've completed; doing another 3 sets of 3 of these exercises and alternating the three that i choose every time. I keep track of everything i do in a nice excel sheet.

I'm kind of worried about my form, since i've never done this before, i could be doing these the wrong way etc but i have studied each exercise carefully and read about them on the net.. but theres no one to spot a mistake.

What im wondering is is it possible to reach my goal weight working out at home, or if i really need to signup for a gym membership(maybe even a personal trainer..)

thanks for any advice in advance!
 
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